Difference between revisions of "CompoundMatrix"
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| − | <tt>'''CompoundMatrix'''</tt> is a [[List of functions|function]] that computes the ''r'' th [https://en.wikipedia.org/wiki/Compound_matrix compound matrix] of a given matrix. | + | <tt>'''CompoundMatrix'''</tt> is a [[List of functions|function]] that computes the ''r'' <sup>th</sup> [https://en.wikipedia.org/wiki/Compound_matrix compound matrix] of a given matrix. |
==Syntax== | ==Syntax== | ||
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==Example== | ==Example== | ||
| − | Taking the | + | Taking the 2<sup>nd</sup> compound matrix involves calculating 2 by 2 minors of the matrix. For a 3 by 4 matrix, the entries for these minors can be indexed by the row index sets {1,2}, {1,3}, and {2,3} and the column index sets {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. The computed values are placed in the resulting compound matrix according to the lexicographic ordering of the index sets. The following code shows an example: |
<syntaxhighlight> | <syntaxhighlight> | ||
>> A = [1, 3, 7, 2; 8, 5, 3, 4; 6, 9, 0, 1] | >> A = [1, 3, 7, 2; 8, 5, 3, 4; 6, 9, 0, 1] | ||
Revision as of 02:40, 23 August 2024
| CompoundMatrix | |
| Computes the compound matrix of a given matrix | |
| Other toolboxes required | none |
|---|---|
| Function category | Miscellaneous |
CompoundMatrix is a function that computes the r th compound matrix of a given matrix.
Syntax
- comp = CompoundMatrix(A, r)
Argument descriptions
- A: A matrix.
- r: An integer denoting the size of the minors to compute.
Example
Taking the 2nd compound matrix involves calculating 2 by 2 minors of the matrix. For a 3 by 4 matrix, the entries for these minors can be indexed by the row index sets {1,2}, {1,3}, and {2,3} and the column index sets {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. The computed values are placed in the resulting compound matrix according to the lexicographic ordering of the index sets. The following code shows an example:
>> A = [1, 3, 7, 2; 8, 5, 3, 4; 6, 9, 0, 1]
>> r = 2
>> compoundMatrix(A, r)
A =
1 3 7 2
8 5 3 4
6 9 0 1
r =
2
ans =
-19 -53 -12 -26 2 22
-9 -42 -11 -63 -15 7
42 -18 -16 -27 -31 3Notice that the size of the resulting matrix is not necessarily the same size as the original matrix. In general, the size of the compound matrix is (m choose r ) by (n choose r ) for an m by n matrix.
Source code
Click here to view this function's source code on github.